Countless phenomena follow a normal distribution and therefor it is perhaps the
ID: 3201642 • Letter: C
Question
Countless phenomena follow a normal distribution and therefor it is perhaps the most important of the theoretical distributions applied to continuous variables. The normal distribution is important to statistical work because most hypothesis tests that are used assume that the random variable being considered has an underlying normal distribution. Using your topic of interest what phenomena might you be interested in measuring as it applies to normal distribution? Be sure you show me you understand not only the principle of the distribution (and subsequent curve) but also how mean and standard deviation might influence or be significant in your proposed area of study.
Explanation / Answer
I am interested in studying the monthly income of all people USA. Some people might have very high income and some will be having very low income. We can assume that the income is distributted normally. In this case, most of the people will have an income that lies closer to the percapita income of the country. Here, per capita income is the mean of the data. The distribution can be assumed to be normal because only the a small portion of people will have a very high income and only a small portion will have a very low income as well. so, the curve with income in x axis and no of people with that particular income on y axis will have shape similar to that of a normal curve (bell shaped curve).
The mean of the data is the point on x axis where on y the curve is at peak. For a standard normal distribution, the number of observation below and above mean will be the same. As the standard deviation increase, it means that the difference between mean and individual observations increase. So, the curve will remain bell shaped, but the curvature reduces and becomes more and more flat as the standard deviation increase. If the standard deviation decrease, the curve become more steeper and finally, if standard deviation is 0, the curve will be a straight line parallel to Y axis, intercepting the x axis at the mean value.